Ideal Gas Equation Of State Research Articles

Investigation on the fusion reaction rate of deuterium and tritium under heterogeneous mixing

Mixing between shell material and gas fuel, caused by hydrodynamic instability, isolated defects, or kinetic effects, is the key to understand the degradation of implosion performance in the research of inertial confinement fusion. Understanding the mixing mechanism and reducing its impact is of extreme importance to achieve the ignition and high gain. The impact of mixing morphology on thermonuclear reaction rate in sub grid level has gradually attracted people’s attention in recent years due to its direct influence on burn rate and fusion process, the study on physical model of thermonuclear reaction rate in different mix morphology has important scientific significance and application value. In the paper, the dependence of thermonuclear reaction rate on mass distribution of different fuel concentrations at sub grid scale is derived. Based on thermodynamic equilibrium and ideal gas equation of state, the physical law of the evolution of the thermonuclear reaction rate with mix morphology under the dominance of diffusion mixing is revealed through analytical formula and numerical solution of diffusion equation in one-dimensional spherical geometry. It is convinced that the mixing amount directly affects the thermonuclear reaction rate by mainly affecting the volume fraction of the fuel, and the mixing diffusion time determined by heterogeneous mixing scale and diffusion coefficient directly affects the evolution behavior of the thermonuclear reaction rate. Furthermore, based on mutual diffusion coefficient obtained from direct simulation of diffusion process by Monte Carlo method, the difference of impact to thermonuclear reaction rate for low-<i>Z</i> Carbon and high-<i>Z</i> gold mixing is quantitatively investigated. Heterogeneous mix size with 0.1 μm, 0.01 μm respectively for the low-<i>Z</i> and high-<i>Z</i> mixing can be treated as atomic mix in burn rate aspect, and heterogeneous mix size with 10 μm, 1 μm respectively for the low-<i>Z</i> and high-<i>Z</i> mixing can be treated as ideal chunk mix in burn rate aspect, and heterogeneous mix size in the middle state needs to be evaluated by using the heterogeneous mixing model of thermonuclear reaction rate in the paper. Finally, the physical model is compared with 3D simulation results of the heterogeneous mixing effect experiment called “MARBLE Campaign” carried out on OMEGA laser facility, which is designed as a separated reactant experiments and capsules are filled with deuterated foam and HT gas pores of different size, covering typical mix morphology from atomic mix to chunk mix, which validate the reliability of the theoretical evaluation about the evolution of mixing morphology and its impact to thermonuclear reaction rate. This work is significant for the design and improvement of inertial confinement fusion mixing effect experiment in China.

Dynamic characteristics of proton exchange membrane fuel cell on a multiple time scale

The current research on the dynamic performance of the proton exchange fuel cell is mostly aimed at the influence of operating parameters on the system, but does not involve with the dynamic characteristics of the cell on a multiple time scale nor the study of the corresponding multiple time scale model. In order to detect the dynamic changes of the proton exchange membrane fuel cell, the effects of various factors in the system on the output performance on different time scales are investigated. The effective partial pressure of oxygen and hydrogen are obtained by the mass diffusion equation and the ideal gas state equation, and the dynamic model is established according to the law of conservation of energy, the law of thermodynamics, and the electrochemical reaction equation. By setting the load mutations with a large/medium/small time scale dynamic duration of 0.6 s, 165 s, and16 min, respectively, the mechanism with which voltage suddenly changes when the load current changes abruptly is studied. Starting from the long time constant during which the dynamic performance takes effect, the control variable is used to analyze the double-layer charge. The influences of layer effect capacitance <i>C</i>, fuel oxidant delay time constant <i>τ</i><sub>e</sub>, and thermodynamic characteristics (temperature <i>T</i>) on the dynamic performance ( initial values of variables: <i>C</i> = 4 F, <i>τ</i><sub>e</sub> = 80 s, and <i>T</i> = 307.7 K) clarify the action intensities on different time scales. With the help of Matlab/Sumlink platform the simulation results are obtained and the correctness and effectiveness of the built model are verified. The simulation results show that the sudden change in voltage is due to the open circuit voltage and Ohmic polarization resistance, and the Ohmic resistance is dominant (the Ohmic overvoltage change value is 2 V, and the open circuit voltage change is 0.05 V), and the <i>C</i> pair dynamics on a small time scale (ms). The performance plays a leading role. Specifically, <i>τ</i><sub>e</sub> has a greater effect on the dynamic characteristics on a medium time scale (s), and <i>T</i> has a stronger effect on a large time scale (10<sup>2</sup>–10<sup>3</sup> s). Based on the above deduction, a multi-time scale model of the battery is derived. The research provides the reference and theoretical support for subsequent battery energy management, evaluation of dynamic performance, and precise control.

Investigation on Coal Skeleton Deformation in CO2 Injection Enhanced CH4 Drainage From Underground Coal Seam

To reveal the evolution law of coal skeleton deformation during the process of CO2 flooding and displacing CH4 in coal seam, a fluid-solid coupling mathematical model of CO2 injection enhanced CH4 drainage was established based on Fick’s law, Darcy’s law, ideal gas state equation, and Langmuir equation. Meanwhile, numerical simulations were carried out by implementing the mathematical model in the COMSOL Multiphysics. Results show that the CH4 content of both regular gas drainage and CO2 enhanced gas drainage gradually decreases with time, and the decreasing rate is high between 10 and 60 days. Compared with regular gas drainage, the efficiency of CO2 enhanced gas drainage is more obvious with greater amount of CH4 extracted out. When coal seam gas is extracted for 10, 60, 120, and 180 days, CH4 content in coal seam is reduced by 5.2, 17.2, 23.6, and 26.7%, respectively. For regular gas drainage, the deformation of coal skeleton is dominated by the shrink of coal matrix induced by gas desorption, and the strain curve shows a continuous downward trend. For CO2 enhanced gas drainage, the strain curve of coal skeleton showed a decrease—rapid increase—slow increase trend. The evolution of permeability is opposite to the evolution of coal skeleton strain. Higher gas injection pressure will lead to a greater coal skeleton strain. The pumping pressure affects the deformation of coal skeleton slightly compared with that of initial water saturation and initial temperature. Greater initial water saturation leads to larger deformation of coal skeleton in the early stage. The strain value of coal skeleton gradually tends to be consistent as gas injection prolongs. Higher initial temperature leads to greater reduction in coal skeleton strain when the gas injection continues. Research achievements provide a basis for the field application of CO2 injection enhanced CH4 drainage in underground coal mines.

A linear stability analysis of compressible hybrid lattice Boltzmann methods

An original spectral study of the compressible hybrid lattice Boltzmann method (HLBM) on standard lattice is proposed. In this framework, the mass and momentum equations are addressed using the lattice Boltzmann method (LBM), while finite difference (FD) schemes solve an energy equation. Both systems are coupled with each other thanks to an ideal gas equation of state. This work aims at answering some questions regarding the numerical stability of such models, which strongly depends on the choice of numerical parameters. To this extent, several one- and two-dimensional HLBM classes based on different energy variables, formulations (primitive or conservative), collision terms and numerical schemes are scrutinized. Once appropriate corrective terms introduced, it is shown that all continuous HLBM classes recover the Navier-Stokes-Fourier behavior in the linear approximation. However, striking differences arise between HLBM classes when their discrete counterparts are analyzed. Multiple instability mechanisms arising at relatively high Mach number are pointed out and two exhaustive stabilization strategies are introduced: (1) decreasing the time step by changing the reference temperature Tr and (2) introducing a controllable numerical dissipation σ via the collision operator. A complete parametric study reveals that only HLBM classes based on the primitive and conservative entropy equations are found usable for compressible applications. Finally, an innovative study of the macroscopic modal composition of the entropy classes is conducted. Through this study, two original phenomena, referred to as shear-to-entropy and entropy-to-shear transfers, are highlighted and confirmed on standard two-dimensional test cases.

Implementation of Direct Acoustic Simulation using ANSYS Fluent

Direct Acoustic Simulation (DAS) is a powerful Computational Aero Acoustics method that obtains hydrodynamic and acoustic solutions simultaneously by solving compressible Navier-Stokes equation together with state equation of ideal gas. Thus, DAS has advantages for cases with flow acoustic coupling and high Mach numbers (). With an increasing demand of massive-scale calculations, a robust numerical solver for DAS is required. ANSYS Fluent is a suitable CFD platform with proven robustness. However, there is no direct implementation of DAS in the current version of ANSYS Fluent. The present study, therefore, aims to investigate an approach for implementing DAS using ANSYS Fluent. Given the acoustic part of fluctuations is much smaller than the hydrodynamic part in amplitude, a DAS solver requires high accuracy and low dissipation. Based on these needs, proper solution methods, spatial discrete methods and boundary conditions are firstly determined through simple calculations of two dimensional propagating plane waves. Afterwards aeroacoustics of a two-dimensional cavity flow at 0.6 is calculated to verify the capability for solving separating flow with the aforementioned set-up. Finally, aeroacoustics of a cylindrical bluff body at a turbulent regime and 0.2 is calculated in three-dimensions to verify the capability for solving turbulent flow using Monotonically Integrated Large Eddy Simulation.

Blast in the one-dimensional cold gas: Comparison of microscopic simulations with hydrodynamic predictions

We study the response of an infinite system of point particles on the line initially at rest to the instantaneous release of energy in a localized region. The blast generates shock waves, and we make a detailed comparison of the density, velocity, and temperature in the growing region between the shock waves predicted by Euler equations for the ideal nondissipative compressible gas and the results of direct microscopic simulations. At long times, the hydrodynamic variables acquire self-similar forms with scaling functions predicted by the Taylor–von Neumann–Sedov (TvNS) blast-wave solution. The scaling functions obtained from the microscopic dynamics show a remarkable agreement with the TvNS predictions, except at the blast core, where the TvNS solution predicts a diverging temperature, which is not observed in simulations. We show that the effect of heat conduction becomes important and present results from a numerical solution of the Navier–Stokes–Fourier equations. A different scaling form is observed in the blast core. Our microscopic model is the one-dimensional hard-point gas with binary mass distribution and alternating masses. This infinitely dilute gas has the ideal gas equation of state and is nonintegrable and known to display fast equilibration.

The research on current rush to air mass in delivery pipeline system with YOUNGS-VOF method

Water hammer with gas often occurs in long delivery pipeline system lager than ordinary water hammer, surface tracking between air and water is important and difficult. In this paper, flow rush to interception air-mass in long water conveyance pipe system is researched on base on surface in between water and gas tracking method of staggered grid dispersed with YOUNGS-VOF, the limited compressibility method of viscous incompressible fluid control equations, and numerical method of ideal gas state equation. The numerical results show that YOUNGS-VOF method can be used to deal with the interface and water hammer is consistent with the theory analysis.

Thermodynamic approach to the T -models

The perfect fluid solutions admitting a group G$_3$ of isometries acting on orbits S$_2$ whose curvature has a gradient which is tangent to the fluid flow (T-models) are studied from a thermodynamic approach. All the admissible thermodynamic schemes are obtained, and the solutions compatible with the generic ideal gas equation of state are studied in detail. The possible physical interpretation of some previously known T-models is also analyzed.

Linear Dynamic Analysis of Free-Piston Stirling Engines on Operable Charge Pressure and Working Frequency along with Experimental Verifications

This paper presents a linear dynamic analysis on operable charge pressure and working frequency of free-piston Stirling engines (FPSE) along with experimental verifications. The equations of motion of the FPSE are formulated as a 2-degree-of-freedom (DOF) vibration system of the power piston (PP) and displacer piston (DP), based on the state equation of ideal gas and the isothermal Stirling cycle model. The dynamic models of FPSE we considered are the 1-DOF simple vibration model of each piston and the 2-DOF root locus model of coupled pistons. We developed a test FPSE for verification of the dynamic models and conducted a series of experiments to measure the dynamic behaviors of PP and DP under varying charge pressures for various masses and stiffnesses of the PP. As a result, both prediction models showed good agreements with experimental results. The 1-DOF vibration model was found to be simple and effective for predicting the operating frequency and charge pressure of FPSE. The root locus method showed reasonable predictions with an operation criterion of the PP–DP phase angle of 90°. In addition, the FPSE was confirmed to operate in resonant oscillations when the DP–PP phase angle is 90°, based on analysis of the force vector diagram of the two pistons.

Power distribution method for a parallel hydraulic-pneumatic hybrid system using a piecewise function

The Benedict-Webb-Rubin model or the ideal gas equation of state alone cannot accurately describe the load model of a parallel hydraulic-pneumatic hybrid system. This paper proposes a load model of the energy recovery system based on a piecewise function considering the load components switching problem under high energy regenerative braking and cruise charging conditions. This model can express the influence of the pre-charge pressure of the hydraulic accumulator and the air compressor speed on the system load power. This is accomplished by detecting the hydraulic accumulator state of charge, the transient temperature of nitrogen, and the transient temperature of the air in the reservoir. The load power of the energy recovery system can be estimated under various working conditions and used to guide the adjustment of the hydraulic pump/motor displacement to adjust the power distribution of the energy recovery system. This can solve the problem of ineffective power distribution and overspeed conditions, as well as fluctuation of the air compressor operation caused by changes in mechanical input power. The method proposed in this paper provides a new technical approach for the configuration of parallel hydraulic-pneumatic hybrid power systems.

On the Oberbeck–Boussinesq approximation for gases

The Oberbeck–Boussinesq (OB) approximation for a compressible fluid in Bénard’s problem geometry is studied. We present a new derivation of the classical and ’extended’ OB models for a fluid obeying the ideal gas state equation by means of an asymptotic limit for vanishing temperature difference. The ‘extended’ OB approximation takes account of the compressibility effects in the energy balance, due to the work of hydrostatic pressure inside the stratified fluid, while the isochoric character of the motion is unchanged. The scaling laws on the material and experimental parameters realizing the asymptotic systems are characterized. Moreover, the ranges of validity of the approximations are described in terms of temperature difference and thickness of the fluid layer and two other characteristic lengths associated to the material parameters. The problem of non-linear stability of the rest state in the extended OB model is traced back to the known stability analysis of the classical OB model by means of a rescaling of the temperature perturbation.

Effects of nitrogen and argon on ammonia-oxygen explosion

The primary task of this work is to clarify ammonia-oxygen explosion characteristics under nitrogen and argon atmosphere. Firstly, the flame behavior and explosion pressure are experimentally obtained. Then their correlation is revealed quantitatively. The thermal, diffusive and chemical analysis is conducted at last. The results demonstrated that the variation tendency of flame propagation velocity (FPV), maximum explosion pressure (MEP) and maximum rate of pressure rise (MRPR) is completely consistent. All index of FPV, MEP and MRPR, becomes increased and decreased with increasing equivalence ratio, continues to decrease with increasing inert gas fraction. All index of FPV, MEP and MRPR under argon atmosphere is totally larger than that under nitrogen atmosphere. By considering the state equation of ideal gas, spherically smooth flame and adiabatic compression, the flame behavior and explosion pressure under nitrogen and argon atmosphere is significantly controlled by laminar burning speed (LBS). As the inert gas fraction and equivalence ratio change, the LBS under nitrogen and argon atmosphere is significantly controlled by adiabatic flame temperature. The joint action of adiabatic flame temperature and thermal diffusivity contributes to the LBS difference.

Simple high order well-balanced finite difference WENO schemes for the Euler equations under gravitational fields

The compressible Euler equations coupled with the gravitational source terms admit a hydrostatic equilibrium state where the gradients of the flux terms can be exactly balanced by those in the source terms. This property of exact preservation of the equilibrium is highly desirable at the discrete level when they are numerically solved. In this study, we design the simple high order well-balanced finite difference weighted essentially non-oscillatory (WENO-R/I) schemes, which base on the WENO reconstruction and interpolation procedures respectively, for this system with an ideal gas equation of state and a prescribed gravitational field. The main idea in achieving the well-balanced property is to rewrite the source terms in a special way and discretize them by using the nonlinear WENO differential operators with the homogenization condition to those for the flux terms. The proposed well-balanced schemes can be proved mathematically to preserve the hydrostatic isothermal and polytropic equilibria states exactly and at the same time maintain genuine high order accuracy. Moreover, the resulting schemes are high efficiency of computation and can be implemented straightforwardly into the existing finite difference WENO code with the Lax-Friedrichs numerical flux for solving the compressible Euler equations. Last but not least, the proposed well-balanced framework also works for a class of moving equilibrium state. Extensive one- and two-dimensional numerical examples are carried out to investigate the performance of the proposed schemes in term of high order accuracy, well-balanced property, shock capturing essentially non-oscillatory and resolving the small perturbation on the coarse mesh resolution.

Modelling of multiple gas transport mechanisms through coal particle considering thermal effects

Multiple gas diffusion mechanisms coexist in the nanopores of coal particle, including Knudsen diffusion, slip flow and transition flow of bulk gas and surface diffusion of adsorbed gas. The contribution of each mechanism to the total gas diffusion quantity varies with gas pressure and pore radius. In this study, a coupled thermal-diffused-mechanical model was constructed considering the multiple gas transport mechanisms. The complex coupling relations among gas adsorption/desorption, gas diffusion field, mechanical deformation field and thermal field during gas diffusion of coal were considered. The contribution of each diffusion mechanisms to the total gas diffusion quantity under variable pressure and pore radius was discussed. Thermal effects of gas diffusion were studied by considering the whole diffusion process as adiabatic. The results show that Knudsen diffusion is dominant in the low-pressure region, regardless of the pore size. In the high-pressure region, the slip flow is dominant when the pore radius is large, while the surface diffusion is dominant when the pore radius is relatively small. The gas diffusion velocity and total diffusion quantity under adiabatic conditions are lower than that under isothermal conditions. But the rate of pressure drop is opposite, which can be explained by the ideal gas equation of state. In reality, the gas diffusion process is neither isothermal nor adiabatic, but between the two states. The thermal effect should be considered in the study of gas diffusion properties.

Improved compressible hybrid lattice Boltzmann method on standard lattice for subsonic and supersonic flows

A D2Q9 Hybrid Lattice Boltzmann Method (HLBM) is proposed for the simulation of both compressible subsonic and supersonic flows. This HLBM is an extension of the model of Feng et al. [1], which has been found, via different test cases, to be unstable for supersonic regimes. To circumvent this limitation, we propose:: (1) a new discretization of the lattice closure correction term that makes possible the simulation of supersonic flows, (2) a corrected viscous stress tensor that takes into account polyatomic gases, and (3) a novel discretization of the viscous heat production term fitting with the regularized formalism. The result is a hybrid method that resolves the mass and momentum equations with an LBM algorithm, and resolves the entropy-based energy equation with a finite volume method. This approach fully recovers the physics of the Navier–Stokes–Fourier equations with the ideal gas equation of state, and is valid from subsonic to supersonic regimes. It is then successfully assessed with both smooth flows and flows involving shocks. The proposed model is shown to be an efficient, accurate, and robust alternative to classic Navier–Stokes methods for the simulation of compressible flows.

Correspondence between Israel-Stewart and first-order causal and stable hydrodynamics for Bjorken-expanding baryon-rich systems with vanishing particle masses

We obtain an exact correspondence between the dynamical equations in Israel-Stewart (IS) theory and first-order causal and stable (FOCS) hydrodynamics for a boost-invariant system with an ideal gas equation of state at finite baryon chemical potential. Explicit expressions for the temperature and chemical potential dependence of the regulators in the FOCS theory are given in terms of the kinetic coefficients and constant relaxation time of the IS theory. Using the correspondence between the IS and FOCS theory, stability conditions for a charged fluid which are known in the FOCS approach are applied and one finds that the IS theory considered is unstable.

Experimental and numerical investigation of high-pressure nitromethane combustion

The burning rate of liquid nitromethane as a function of pressure is known to exhibit slope breaks, following Saint-Robert's law only in limited regions of pressure. The present paper presents experimental and modeling results with the objective to better understand this behavior. A new experimental facility is used to visually observe the combustion process from 3 to 101 MPa allowing for measurement of burning rates in tubes of various diameters with high-speed cinematography. A series of modeling calculations are performed increasing in complexity first studying vapor phase flame propagation with the ideal gas equation of state and then a real gas equation of state. These results are compared with previously published predictions of the liquid regression rate using the same kinetic model and ideal gas equation of state. Theory indicates that, at high pressures, the freely propagating vapor-phase flame speed should agree with liquid regression rates. Combined, these results enable further insight into the mechanisms for the slope breaks and complex burning behavior. Three regimes were identified in the burning rate as a function of pressure. A low-pressure regime with pressure exponent of 1.16 exists where burning occurs with a distinct interface between liquid and gas. At approximately 18 MPa, an abrupt increase in burning rate occurs that is associated with the critical point of the mixture of nitromethane and near-surface species producing pressure exponents ranging from 2–10. Above this pressure, the loss of surface tension induces surface waves and large-scale hydrodynamic instabilities. With increasing pressure, burning rates continue to increase with pressure but with a gradual decrease in pressure exponent towards a value of ∼0.75. At the highest pressure the large-scale instabilities disappear, and the flame propagates with a turbulent cellular front, the speed of which depends upon the tube diameter.

Near-field models and simulations of pellet ablation in tokamaks

Detailed numerical studies of the ablation of a single neon pellet in the plasma disruption mitigation parameter space have been performed. Simulations were carried out using FronTier, a hydrodynamic/low magnetic Reynolds number MHD code with explicit tracking of material interfaces. FronTier's physics models resolve the pellet surface ablation and the formation of a dense, cold cloud of ablated material, the deposition of energy from hot plasma electrons, the expansion of the ablation cloud along magnetic field lines, and the radiation losses. A local thermodynamic equilibrium model based on Saha equations has been used to resolve atomic processes in the cloud and Redlich–Kwong corrections to the ideal gas equation of state for cold and dense gases, which have been used near the pellet surface. The FronTier pellet code is a next generation of the code described in [R. Samulyak et al., Nucl. Fusion 47, 103 (2007)]. It has been validated against the semi-analytic improved neutral gas shielding model in the 1D spherically symmetric approximation. Main results include quantification of the influence of atomic processes and Redlich–Kwong corrections on the pellet ablation in spherically symmetric approximation and verification of analytic scaling laws in a broad range of pellet and plasma parameters. Using axially symmetric MHD simulations, the properties of ablation channels and the reduction of pellet ablation rates in magnetic fields of increasing strength have been studied. While the main emphasis has been given to neon pellets for the plasma disruption mitigation, selected results on deuterium fueling pellets have also been presented.

Analysis of the application of ideal gas equation of state

In nature, the molecules of real gas have a certain volume and have interaction force with each other. It is difficult to find the molecular motion law of real gas because of its complex properties. An ideal gas is an imaginary substance that does not exist in reality. Its molecules are elastic, non volume particles, and there is no interaction among them. This kind of gas is simple in nature and easy to be analyzed and calculated by simple mathematical relation. The introduction of the concept of ideal gas greatly simplifies the analysis of some thermodynamic problems.

Lattice Boltzmann simulation of near/supercritical CO2 flow featuring a crossover formulation of the equation of state

In this work, we have incorporated a crossover equation of state into the pseudopotential multiphase Lattice Boltzmann Model (LBM) to improve the prediction of thermodynamic properties of fluids and their flow in near-critical and supercritical regions. Modeling carbon dioxide (CO2) properties in these regions is of increasing interest for industrial processes such as CO2 storage and heat transfer where CO2 is used as a working fluid. Despite the importance of accurately modeling near-critical and supercritical fluids, popular classical cubic equations of state (EoS) are not accurate. The proposed crossover EoS is a proven hybrid equation which uses the original classical EoS far from the critical point where it is valid, and near the critical point, it asymptotically switches to using non-analytic scaling laws. It also transforms into the ideal gas EoS as the density approaches zero. In order to demonstrate the validity and versatility of the crossover approach in the prediction accuracy of LBM in near-critical flows, this formulation was incorporated into the Peng-Robinson (P-R) EoS. First, 2D static droplets of CO2 and water at vapor-liquid equilibrium were modeled using both P-R EoS and its crossover formulation, and the numerically predicted results were then compared against the experimental data. The results demonstrate that the model accuracy in representing the thermodynamic behavior of the fluid in near-critical region is improved after adopting the crossover formulation with respect to the classical analytical EoS. The crossover P-R EoS was further applied to study several two-phase CO2 flows in mini-channels at near-critical temperatures. The flow patterns showed a good qualitative agreement with the experimental data in the near-critical region. The study is further extended to multi-component multiphase systems, specifically to water droplet penetration into porous media filled with CO2.